1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the fluid content of earth formations. More specifically, the invention is related to methods for calculating fractional volumes of various fluids disposed in the pore spaces of earth formations where these earth formations include laminations of shale or laminated shale distribution with reservoir rock that may include dispersed shales.
2. Background of the Art
A significant number of hydrocarbon reservoirs include deep water turbidite deposits that consist of thin bedded, laminated sands and shales. A common method for evaluating the hydrocarbon content of reservoirs is the use of resistivity measurements. In interpretation techniques known in the art, typically one or more types of porosity-related measurement will be combined with measurements of the electrical resistivity (or its inverse, electrical conductivity) of the earth formations to infer the fluid content within the pore spaces of the earth formations. The fractional volumes of connate water and hydrocarbons can be inferred from empirical relationships of formation resistivity Rt with respect to porosity and connate water resistivity such as, for example, the well known Archie relationship. In the Archie relationship fractional volume of water in the pore space is represented, as shown in the following expression, by Swxe2x80x94known as xe2x80x9cwater saturationxe2x80x9d:                               S          w          n                =                                            R              0                                      R              t                                =                                    1                              R                t                                      ⁢                          xe2x80x83                        ⁢                                          a                ⁢                                  xe2x80x83                                ⁢                                  R                  w                                                            φ                m                                                                        (        1        )            
where a and m are empirically determined factors which relate the porosity (represented by "PHgr") to the resistivity of the porous rock formation when it is completely water-saturated (R0), Rw represents the resistivity of the connate water disposed in the pore spaces of the formation, and m represents an empirically determined xe2x80x9cicementationxe2x80x9d exponent, n is the saturation exponent.
Relationships such as the Archie formula shown in equation (1) do not work very well when the particular earth formation being analyzed includes some amount of extremely fine-grained, clay mineral-based components known in the art as xe2x80x9cshalexe2x80x9d. Shale typically occurs, among other ways, in earth formations as xe2x80x9cdispersedxe2x80x9d shale, where particles of clay minerals occupy some of the pore spaces in the hydrocarbon-bearing earth formations, or as laminations (layers) of clay mineral-based rock interleaved with layers of reservoir-type rock in a particular earth formation.
In the case of dispersed shale, various empirically derived relationships have been developed to calculate the fractional volume of pore space which is capable of containing movable (producible) hydrocarbons. The fractional volume of such formations which is occupied by dispersed shale can be estimated using such well logging devices as natural gamma ray radiation detectors. See for example, M. H. Waxman et al, xe2x80x9cElectrical Conductivities in Oil Bearing Shaly Sandsxe2x80x9d, SPE Journal, vol. 8, no. 2, Society of Petroleum Engineers, Richardson, Tex. (1968).
In the case of laminated shale, the layers sometimes are thick enough to be within the vertical resolution of, and therefore are determinable by, well logging instruments such as a natural gamma ray detector. In these cases, the shale layers are determined not to be reservoir rock formation and are generally ignored for purposes of determining hydrocarbon content of the particular earth formation. A problem in laminated shale reservoirs is where the shale laminations are not thick enough to be fully determined using gamma ray detectors and are not thick enough to have their electrical resistivity accurately determined by electrical resistivity measuring devices known in the art.
Sands that have high hydrocarbon saturation are typically more resistive than shales. In reservoirs consisting of thin laminations of sands and shales, conventional induction logging tools greatly underestimate the resistivity of the reservoir: the currents induced in the formation by the logging tool flow preferentially through the conductive shale laminations creating a bias towards a higher formation conductivity. This could lead to an underestimation of hydrocarbon reserves.
One method for estimating hydrocarbon content of earth formations where shale laminations are present was developed by Poupon. See A. Poupon et al, xe2x80x9cA Contribution to Electrical Log Interpretation in Shaly Sandsxe2x80x9d, Transactions AIME, Vol. 201, pp. 138-145 (1959). Generally the Poupon relationship assumes that the shale layers affect the overall electrical conductivity of the earth formation being analyzed in proportion to the fractional volume of the shale layers within the particular earth formation being analyzed. The fractional volume is typically represented by Vsh (shale xe2x80x9cvolumexe2x80x9d). Poupon""s model also assumes that the electrical conductivity measured by the well logging instrument will include proportional effects of the shale layers, leaving the remainder of the measured electrical conductivity as originating in the xe2x80x9ccleanxe2x80x9d (non-shale bearing) reservoir rock layers as shown in the following expression:                               1                      R            t                          =                                            (                              1                -                                  V                  sh                                            )                        ⁢                          xe2x80x83                        ⁢                                          (                                                      a                    ⁢                                          xe2x80x83                                        ⁢                                          R                      w                                                                            φ                    m                                                  )                                            -                1                                      ⁢                          xe2x80x83                        ⁢                          S              w              n                                +                                    V              sh                                      R              sh                                                          (        2        )            
where Rt represents the electrical resistivity (inverse of conductivity) in the reservoir rock layers of the formation and Rsh represents the resistivity in the shale layers.
The analysis by Poupon overlooks the effect of anisotropy in the resistivity of a reservoir including thinly laminated sands and shales. Use of improper evaluation models in many cases may result in an underestimation of reservoir producibility and hydrocarbon reserves by 40% or more as noted by van den Berg and Sandor. Analysis of well logging instrument measurements for determining the fluid content of possible hydrocarbon reservoirs includes calculating the fractional volume of pore space (xe2x80x9cporosityxe2x80x9d) and calculating the fractional volumes within the pore spaces of both hydrocarbons and connate water. As noted above, Archie""s relationship may be used.
In thinly laminated reservoirs where the wavelength of the interrogating electromagnetic wave is greater than the thickness of the individual layers, the reservoir exhibits an anisotropy in the resistivity. This anisotropy may be detected by using a logging tool that has, in addition to the usual transmitter coil and receiver coil aligned along with the axis of the borehole, a receiver or a transmitter coil aligned at an angle to the borehole axis. Such devices have been well described in the past for dip determination. See, for example, U.S. Pat. No. 3,510,757 to Huston and U.S. Pat. No. 5,115,198 to Gianzero,
U.S. Pat. No. 5,656,930 issued to Hagiwara discloses a method of determining the horizontal resistivity, the vertical resistivity, and the anisotropy coefficient of a subterranean formation by means of an induction type logging tool positioned in a deviated borehole within the subterranean formation. In a preferred implementation, the induction type logging tool is first calibrated to determine a proportionality constant. A predetermined relationship between the proportionality constant, the phase shift derived resistivity, the attenuation derived resistivity, the horizontal resistivity, the vertical resistivity, and the anisotropy coefficient is then generated and stored in the memory of a programmed central processing unit. During an induction logging operation, the phase shift derived resistivity and attenuation derived resistivity are then received and processed by the programmed central processing unit in accordance with the predetermined relationship to generate the horizontal resistivity, the vertical resistivity, and the anisotropy coefficient. These measured values of horizontal and vertical resistivities when combined with a predetermined relationship between the horizontal resistivity, the vertical resistivity, the net/gross ratio, and the ratio of the sand layer resistivity to the shale layer resistivity make it possible to obtain a net/gross ratio. However, there are many laminated reservoirs in which the sands may include dispersed shales. Interpretation of formation water saturation in such reservoirs can be in error if the combined effects of laminations, dispersed shales within the sand, and possible intrinsic anisotropy of the shales is not considered.
A xe2x80x9cdual waterxe2x80x9d model was developed initially by Clavier, et al., 1977 and 1984. This petrophysical model was later modified and xe2x80x9csimplifiedxe2x80x9d by Coates, Boutemy, and Clavier, 1982, and Coates, Schultz, and Throop, 1982, which was subsequently marketed as Schlumberger Cyberlook(trademark) and VOLAN(trademark) xe2x80x98dual waterxe2x80x99 analysis, respectively. Coates and Howard, 1992, used this technique in a further simplified analysis method called MIRIAN(trademark) (Numar) where the Archie parameters for cementation exponent xe2x80x98mxe2x80x99 and saturation exponent xe2x80x98nxe2x80x99 are combined into a single, empirically derived textural parameter xe2x80x98wxe2x80x99 based on a permeability model published by Coates, et al., 1982. These models lack the ability to physically represent the shale distribution (laminar, dispersed, structural) in shaly sand formations and are dependent on empirical transforms, based on local experience and empirically derived data to resolve the petrophysical effects of shale distribution in xe2x80x98shaly sandxe2x80x99 formations. These limitations result from the single resistivity scalar measurements on which these models are based and the use of xe2x80x98bulk volumexe2x80x99 or averaged wireline porosity tool data.
Patchett and Herrick, 1982, described a volumetrically correct general petrophysical model by combining the Poupon, 1954 laminar shale saturation equation with the WS dispersed shale equation. However, this model was based on a single, scalar horizontal resistivity measurement that is dominated by the parallel conductivity effects of the laminar shales in shaly sand formations. This results in a very low confidence level in the subsequent analysis in any formation that has significant volumes of laminar shale. Patchett and Herrick noted that the laminar sand fraction porosity must be determined using a Thomas-Stieber, 1975, (TS) approach and not a bulk volume shale corrected xe2x80x9ceffective porosityxe2x80x9d as is typically done with traditional empirical methods as used by Ruhovets and Fertl, 1982, in the CLASS(trademark) model.
Juhasz, 1981, proposed a xe2x80x98dual waterxe2x80x99 form of the WS equation and discussed the proper use of the TS porosity model. However, again lacking any quantitative method to discriminate volumes of laminar and dispersed shale volumes, Juhasz proposed that a bulk volume shale bound water saturation term, xe2x80x9cQvnxe2x80x9d, which could be derived from log data and to replace the WS Bxe2x80xa2Qv shale conductivity term. Corrections for shale effects were then applied to the calculated xe2x80x98bulk volumexe2x80x99 water saturation on a xe2x80x98net payxe2x80x99 basis using a simple derivation of the TS shale distribution model. Juhasz did not show how to correct for situations where both laminar and dispersed shale occurred together, simply stating that this was xe2x80x98beyond the scope of a simple modelxe2x80x99. His discussions on the theory and basis for both the TS and WS model developed at Shell research were correct. However, Juhasz""s final implementation of the petrophysical model exhibited the same shortcomings of all xe2x80x98bulk volume shalexe2x80x99 models in properly characterizing shaly formations. Juhasz""s technical discussions in his 1979, 1981, and 1986 papers, on Qv, effective porosity, bound water distribution as a function of shale type, proper correction of porosity for shale distribution, and dispersed shale xe2x80x98bound water conductivityxe2x80x99 form the basis of a new xe2x80x98tensor dual waterxe2x80x99 method proposed herein. This new method is combined with the xe2x80x98tensor modelxe2x80x99 to determining the dispersed shale bound water conductivity, Cwb, from laminar shale corrected cross plots or direct substitution of Qv determined from the Hill, Shirley, and Klein, 1975, equation. This model correctly describes the bound water conductivity component, Cwb, isolated specifically to the dispersed shale fraction. This method is shown to be theoretically correct and conceptually equivalent to the WS Bxe2x80xa2Qv dispersed shale conductivity term.
There is a need for a method of determining the properties of a laminat ed reservoir that includes shales, clean sands and sands having dispersed clay therein. Such a method should preferably determine the water saturation of the sands in order to give a more accurate estimate of the productive capacity of the reservoir. Such a method should preferably be consistent with the Waxman-Smits model for dispersed shale as well as the dual-water model for the bound water in a reservoir. Such a method should preferably make as few assumptions as possible about the properties of the sands and the shales. The present invention satisfies this need.
The present invention is method of accounting for the distribution of shale and water in a reservoir including laminated shaly sands using vertical and horizontal conductivities derived from multi-component induction data. Along with an induction logging tool, data may also be acquired using a borehole resistivity imaging tool. The data from the borehole resistivity imaging tool give measurements of the dip angle of the reservoir, and the resistivity and thickness of the layers on a fine scale. The measurements made by the borehole resistivity imaging tool are calibrated with the data from the induction logging tool that gives measurements having a lower resolution than the borehole resistivity imaging tool. A tensor petrophysical model determines the laminar shale volume and laminar sand conductivity from vertical and horizontal conductivities derived from the log data. The volume of dispersed shale, the total and effective porosities of the laminar sand fraction as well as the effects of clay-bound water in the formation are determined.
The present invention is a method for determination of laminar sand conductivity using vertical and horizontal conductivity components measured with the a suitable logging tool such as a transverse induction tool or a wave propagation tool. For convenience, these measurements will be referred to as xe2x80x9cTILT measurementsxe2x80x9d or xe2x80x9c3-D induction measurementsxe2x80x9d and it is to be understood that any method of measuring horizontal and vertical resistivities may be used. In one embodiment of the invention, the sand and the laminar shale are assumed to be isotropic. In a second embodiment of the invention, the sand is assumed to be isotropic while the laminar shale is assumed to be anisotropic. In a third embodiment of the invention, both the sand and the laminar shale are anisotropic.
For the case where both the sand and the laminar shale are isotropic, the laminar shale volume must be determined using an xe2x80x98externalxe2x80x99 method such as a resistivity imaging tool or from a Thomas Stieber (TS) shale distribution model. The laminar sand conductivity component is determined in all cases from a tensor petrophysical model using the transverse induction measurements. The total and effective porosity of the laminar sand fraction must be determined using the methodology developed by TS and uses either the laminar shale volume from TILT and/or the TS model calculated laminar shale volume.
These laminar sands, interbedded with the laminar shales determined from transverse logging data, generally contain a second, pore filling shale fraction that is termed xe2x80x9cdispersed shalexe2x80x9d. This shale fraction adds a second xe2x80x98parallelxe2x80x99 conductivity pathway through the pore space that increases the xe2x80x98apparentxe2x80x99 total conductivity of the sand versus what would be measured if the sands were only to contain conductive formation water xe2x80x98brinesxe2x80x99. This effect has been well documented by Hill and Milbum, 1955, Waxman and Smits 1968, Hill, Shirley, and Klein, 1975, Thomas 1976, Juhasz, 1979, and is quantified in the widely used WS water saturation equation. Hill, Shirley and Klein (HSK) demonstrated that this conductivity term, Qv, could be empirically approximated if the salinity of the formation brine, in equivalents NaCl was known and the shale bound water volume was known.
Although TS and Juhasz demonstrated how to calculate total and effective porosity of the laminar sand fraction, they did not extend this to the calculation of shale bound water, which is       (                  φ                  total          ⁢                      -                    ⁢          lamrsand                    ·              φ                  effective          ⁢                      -                    ⁢          lamrarsand                      )        φ          total      ⁢              -            ⁢      lamrsand      
Although this is intuitive and used in a bulk volume analysis in xe2x80x98traditional bulk volume methodsxe2x80x99, it is critical that the laminar sand fraction of shale bound water be determined ONLY from laminar sand properties to be correct. Secondly, and more importantly, the laminar shale bound water volume cannot be used in the calculation of sand fraction shale bound water volume or the HSK Qv. The tensor petrophysical model correctly removes this component and correctly calculates the laminar sand fraction conductivity, porosities, and dispersed shale bound water volume.
A second method of determining the dispersed shale bound water volume is used in the present invention when the clay bound water (CBW) volume is measured directly. This may be obtained from Nuclear Magnetic Resonance measurements wherein the distribution of relaxation times may be used to give the CBW using known methods. By calibrating the maximum CBW to 100% shale (CBWshale), the ratio of CBW to shale volume is determined. The TILT laminar shale volume times the CBWshale gives the laminar shale CBW (CBWlaminar) in any interval. By subtracting CBWlaminar component from the total NMR measured CBW, the remaining CBW, by definition, is the dispersed shale bound water volume, CBWdispersed. This is a direct solution without defining the clay/shale parameters of the dispersed component, which has always been a problem in petrophysical analysis. Thus Qv of the laminar sand fraction can be determined directly and quantitatively from the TILT laminar shale volume and NMR CBW and results in the correct results for water saturation of the laminar sand fraction using the Waxman-Smits (WS) equation. This method correctly determines the laminar and dispersed shale volume components, thus reducing the volumetric analysis to a purely xe2x80x98dispersed shaly sand problemxe2x80x99. This is a xe2x80x98theoreticallyxe2x80x99 correct way to use the WS method and provides a direct solution for Qv from NMR CBW data.
The present invention is a volumetrically correct petrophysical model to use these published methodologies. Methods published by Patchett-Herrick, 1982, only postulated the correction of the WS equation for laminar shale conductivity based on the Poupon, 1954, equation and only footnoted that traditional xe2x80x98bulk volumexe2x80x99 total or effective porosity was incorrect. They did not postulate on how to determine laminar shale volume, dispersed shale Qv, or dispersed shale bound water volume and conductivity. Prior to the invention of, laminar shale volume could only be determined indirectly from the TS model. The Juhasz, 1981, xe2x80x9cNormalized Qvxe2x80x9d (Swb) model incorrectly uses the xe2x80x98bulk volume shalexe2x80x99 as does the Cyberlook dual water and suffers from the inherent inaccuracy associated with applying the laminar shale properties to the pore filling, dispersed shales
A dual water form of the WS equation is disclosed based on the Juhasz, 1981 publication. Juhasz presented a substitution of the Bxe2x80xa2Qv term in the WS equation with the equivalent xe2x80x98dual waterxe2x80x99 terms Cwb and Swb, the clay bound water conductivity and clay bound water saturation, respectively. Juhasz demonstrated that by graphically presenting the WS equation, that when Juhasz"" Qvn (Swb), the shale bound water saturation is equal to 1, Bxe2x80xa2Qv=Cwbxe2x88x92Cw (where Cw is the conductivity of the xe2x80x98freexe2x80x99 formation water).
The present invention uses the HSK equation to directly replace Qv and the Cwb term solved for. In the xe2x80x98traditional dual water modelxe2x80x99, the Cwb term is approximated from the conductivity of the laminar shales adjacent to the sands of interest. This is incorrect because the bedded, laminar shales are generally of different clay type and bound water volume than dispersed shales. Laminar shale are xe2x80x98detritalxe2x80x99 or formed from the transport and deposition of clay minerals, silt, and other materials. Dispersed xe2x80x98shalesxe2x80x99 are frequently authogenic, forming from chemical processes after the time of deposition of the sands as well as detrital. Therefore, the determination of dispersed shale conductivity has been xe2x80x98problematicxe2x80x99 and use of improper values of Cwb has predominated, i.e., the xe2x80x98Cyberlook methodxe2x80x99. By demonstrating that equivalent values of Cwb and Qv result in the same water saturation, a unified petrophysical model results from what were once believed to be xe2x80x98incompatiblexe2x80x99. If Bxe2x80xa2Qv is used in a WS saturation analysis, the equivalent Cwb can be calculated and plotted, showing the variation in Cwb as a function of both clay bound water volume and conductivity (equivalent to CEC, the cation exchange capacity). This will demonstrate that the Cwb from laminar shale is incorrect and provide further evidence that dispersed shales are of different composition. There is no longer an argument which model is correct, WS or xe2x80x98dual waterxe2x80x99. The only question is which xe2x80x98dual waterxe2x80x99 model is correct. One that uses the correct dispersed shale volume and bound water conductivity, the tensor dual water model, or one that incorrectly uses the laminar shale conductivity and xe2x80x98bulkxe2x80x99 shale bound water volume, the xe2x80x98Cyberlook(trademark)xe2x80x99 or MIRAIN(trademark) model, which cannot possibly describe the laminar sand fraction properties correctly. The tensor petrophysical model can be used to correctly apply this new xe2x80x98dual waterxe2x80x99 theory because it correctly partitions the laminar and dispersed shale volumes and correctly determines the dispersed shale conductivity based on the measured and accepted industry methodologies of WS, HSK, and Juhasz.
Since the present invention is a theoretically correct xe2x80x98substitution of termsxe2x80x99 for the WS equation, the clay conductivity corrected electrical parameters xe2x80x98a*xe2x80x99, xe2x80x98m*xe2x80x99, xe2x80x98n*xe2x80x99 are correct and are not changed. Again, it must be stressed that only the sand fraction, corrected for laminar shale conductivity and porosity effects, can be used to determine these parameters. Therefore, CEC determined from crushed samples using the xe2x80x98wet chemistryxe2x80x99 titration methods cannot be correctly used with this model and is incorrect. CEC must be determined from Co-Cw or membrane potential methods.